Triangular Numbers and Their Inherent Properties
Chris Zheng, Jeffrey Zheng · 2018
Abstract A method to classify one-dimensional binary sequences using three parameters intrinsic to the sequence itself is introduced. The classification scheme creates combinatorial patterns that can be arranged in a two-dimensional triangular structure. Projections of this structure contain interesting properties related to the Pascal triangle numbers. The arrangement of numbers within the triangular structure has been named “triangular numbers”, and the essential parameters, elementary equation, and sequencing schemes are discussed as well as visualizations of sample distributions, special cases, and search results. We believe this to be a novel finding as sequences generated using this method are not contained in the On-Line Encyclopedia of Integer Sequences or OEIS.